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Dynamical simulation of electron backscatter diffraction (EBSD) patterns of imperfect crystals
(2012)
We demonstrate the determination of crystal chirality using electron backscatter diffraction (EBSD) in the scanning electron microscope. The chirality of a-quartz as a space-group-dependent property is verified via direct comparison of experimental diffraction features to simulations using the dynamical theory of electron diffraction.
Analysis of Kikuchi band contrast reversal in electron backscatter diffraction patterns of silicon
(2010)
We analyze the contrast reversal of Kikuchi bands that can be seen in electron backscatter diffraction (EBSD) patterns under specific experimental conditions. The observed effect can be reproduced using dynamical electron diffraction calculations. Two crucial contributions are identified to be at work: First, the incident beam creates a depth distribution of incoherently backscattered electrons which depends on the incidence angle of the beam. Second, the localized inelastic scattering in the outgoing path leads to pronounced anomalous absorption effects for electrons at grazing emission angles, as these electrons have to go through the largest amount of material. We use simple model depth distributions to account for the incident beam effect, and we assume art exit angle dependent effective crystal thickness in the dynamical electron diffraction calculations. Very good agreement is obtained with experimental observations for silicon at 20 key primary beam energy.
Since the BSE signal depends on many factors, like the chemistry of the phase and the acceleration voltage, the size and position of the detector array is (slightly) different from phase to phase so that an (iterative) post-processing of the stored patterns is highly recommended. The derived BSE signal can be used for phase assignment in high resolution and high speed maps when EBSD fails and/or EDS (energy dispersive spectroscopy) needs too much time for a suitable and parallel signal acquisition.
We present special applications of electron backscatter diffraction (EBSD) which aim to overcome some of the limitations of this technique as it is currently applied in the scanning electron microscope. We stress that the raw EBSD signal carries additional information which is useful beyond the conventional orientation determination. The background signal underlying the backscattered Kikuchi diffraction (BKD) patterns reflects the chemical composition and surface topography but also contains channeling-in information which is used for qualitative real-time orientation imaging using various backscattered electron signals. A significantly improved orientation precision can be achieved when dynamically simulated pattern are matched to the experimental BKD patterns. The breaking of Friedel’s rule makes it possible to obtain orientation mappings with respect to the point-group symmetries. Finally, we discuss the
determination of lattice parameters from individual BKD
patterns. Subgrain structure in a single quartz grain. The increased noise level in the left map reflects the lower precision of a standard orientation determination using band detection by the Hough transform. The right map results from the same experimental raw data after orientation refinement using a pattern matching approach. The colors correspond an adapted inverse pole figure color key with a maximum angular deviation of about 2° from the mean orientation.
The kinetic energy of keV electrons backscattered from a rutile (TiO2) surface depends measurably on the mass of the scattering atom. This makes it possible to determine separately the angular distribution of electrons backscattered elastically from either Ti or O. Diffraction effects of these backscattered electrons inside the rutile crystal lead to the formation of Kikuchi patterns. The element-resolved Kikuchi patterns of Ti and O differ characteristically, but each can be described fairly well in terms of the dynamical theory of diffraction. Qualitatively, much of the differences can be understood by considering the relative arrangement of the Ti and O atoms with respect to planes defined by the crystal lattice.
In order to understand the physical and chemical properties of advanced materials, functional molecular adsorbates, and protein structures, a detailed knowledge of the atomic arrangement is essential. Up to now, if subsurface structures are under investigation, only indirect methods revealed reliable results of the atoms’ spatial arrangement. An alternative and direct method is three-dimensional imaging by means of holography. Holography was in fact proposed for electron waves, because of the electrons’ short wavelength at easily accessible energies. Further, electron waves are ideal structure probes on an atomic length scale, because electrons have a high scattering probability even for light elements. However, holographic reconstructions of electron diffraction patterns have in the past contained severe image artifacts and were limited to at most a few tens of atoms. Here, we present a general reconstruction algorithm that leads to high-quality atomic images showing thousands of atoms. Additionally, we show that different elements can be identified by electron holography for the example of FeS₂ .
Crystal structures that show a broken symmetry in their cubic and hexagonal modifications are of great relevance for optoelectronic and photonic applications. This is why methods which are sensitive to non-centrosymmetric structures are important for analysis of these materials in technological applications.
Using channeling-enhanced energy-dispersive X-ray spectroscopy (EDX), we demonstrate polarity sensitive orientation determination of a non-centrosymmetric crystal in the scanning electron microscope. The authors observe a characteristic asymmetry in the channeling-enhanced, angle-dependent EDX data of a GaAs sample, which is in good agreement to simulations using the dynamical theory of diffraction for the incident electron beam. This allows us to assign the orientation of the GaAs crystal according to the non-centrosymmetric point group. The method shown here overcomes the limitation of a reduced point-group sensitivity of electron backscatter diffraction Patterns and electron channeling patterns for crystalline phases that contain atoms of approximately equal electron scattering cross sections.
EBSD is nowadays a common technique for the characterization of crystalline microstructures in scanning electron microscopy. The diffraction patterns are often interpreted by superimposing individual Kikuchi bands which are geometrically described by band edges derived from Braggs law. For the typically very simple crystal structures of technically applied materials, such a simplification of the Kikuchi pattern interpretation works sufficiently well, especially for orientation determinations as a main application of EBSD. The more complex crystal structures, however, are a challenge for EBSD indexing routines which in such cases often fail unpredictably. The use of only the intensities of single reflectors for a description of the Kikuchi band intensity and as a cut-off criterion for a pre-selection of the strongest bands are not satisfactory. Often the result will match too many phases, or there are certain deviations in the intensity prediction which must be adapted manually. This is already problematic if one is absolutely sure that the patterns are originating from the expected phase and it becomes a very questionable procedure for an unknown phase.
Different models of Kikuchi pattern formation are compared with respect to their applicability to noncentrosymmetric crystals, and the breakdown of Friedel's rule in experimental electron backscatter diffraction (EBSD) patterns is discussed. Different AIIIBV semiconductor materials are used to evaluate the resulting asymmetry of Kikuchi band profiles for polar lattice planes. By comparison with the characteristic etch pit morphology on a single-crystal surface, the polar character of the measured lattice planes can be assigned absolutely. The presented approach enables point-group-resolved orientation mapping, which goes beyond the commonly applied Laue group analysis in EBSD.
We demonstrate an approach to overcome Kikuchi pattern misindexing problems caused by crystallographic pseudosymmetry in electron backscatter diffraction (EBSD) measurements. Based on the quantitative comparison of experimentally measured Kikuchi patterns with dynamical electron diffraction simulations, the algorithm identifies the best-fit orientation from a set of pseudosymmetric candidates. Using measurements on framboidal pyrite (FeS2) as an example, we also show the improvement of the orientation precision using this approach.
We demonstrate polarity-sensitive orientation mapping of non-centrosymmetric phases by Electron Backscatter Diffraction (EBSD). The method overcomes the restrictions of kinematic orientation determination by EBSD, which is limited to the centro-symmetric Laue-groups according to Friedel's rule. Using polycrystalline GaP as an example, we apply a quantitative pattern matching approach based on simulations using the dynamical theory of electron diffraction. This procedure results in a distinct assignment of the local orientation according to the non-centrosymmetric point group of the crystal structure under investigation.
The investigation of the microstructure in functional, polycrystalline thin films is an important contribution to the enhanced understanding of structure–property relationships in corresponding devices. Linear and planar defects within individual grains may affect substantially the performance of the device. These defects are closely related to strain distributions. The present work compares electron and X-ray diffraction as well as Raman microspectroscopy, which provide access to microstrain distributions within individual grains. CuInSe₂ thin films or solar cells are used as a modelsystem. High-resolution electron backscatter diffraction and X-ray microdiffraction as well as Ramanmicrospectroscopy were applied for this comparison. Consistently, microstrain values were determined of the order of 10⁻⁴ by these three techniques. However,only electron backscatter diffraction, X-ray microdiffraction exhibit sensitivities appropriate for mapping local strain changes at the submicrometer level within individual grains in polycrystalline materials.
Kikuchi diffraction patterns can provide fundamental information about the lattice metric of a crystalline phase. In order to improve the possible precision and accuracy of lattice parameter determination from the features observed in Kikuchi patterns, some useful fundamental relationships of geometric crystal-lography are reviewed, which hold true independently of the actual crystal symmetry. The Kikuchi band positions and intersections and the Kikuchi band widths are highly interrelated, which is illustrated by the fact that all lattice plane trace positions of the crystal are predetermined by the definition of only four traces. If, additionally, the projection centre of the gnomonic projection is known, the lattice parameter ratios and the angles between the basis vectors are fixed. A further definition of one specific Kikuchi band width is sufficient to set the absolute sizes of all lattice parameters and to predict the widths of all Kikuchi bands. The mathematical properties of the gnomonic projection turn out to be central to an improved interpretation of Kikuchi pattern data, emphasizing the importance of the exact knowledge of the projection centre.
We discuss the application of EBSD for the analysis of structural features of magnetite and hematite relevant in the topotactic growth of both phases. The orientation relationships of both phases are investigated using characteristically related sets of Kikuchi patterns, which were collected from topotactically intergrown hematite variants and their parent magnetite crystal grain. We address the hexagonal description of trigonal and cubic phases with respect to crystallographic relationships. The combination of locally resolved EBSD measurements and microstructural investigations thus offers a promising opportunity to evaluate orientation relationships and intergrowth between magnetite and hematite.
Advanced structural characterisation techniques which are rapid to use, non-destructive and structurally definitive on the nanoscale are in demand, especially for a detailed understanding of extended-defects and their influence on the properties of materials. We have applied the electron
backscatter diffraction (EBSD) technique in a scanning electron microscope to non-destructively
characterise and quantify antiphase domains (APDs) in GaP thin films grown on different (001)Si substrates with different offcuts. We were able to image and quantify APDs by relating the asymmetrical intensity distributions observed in the EBSD patterns acquired experimentally and comparing the same with the dynamical electron diffraction simulations. Additionally mean angular error maps were also plotted using automated cross-correlation based approaches to image APDs.
Samples grown on substrates with a 4° offcut from the [110] do not show any APDs, whereas samples grown on the exactly oriented substrates contain APDs. The procedures described in our work can be
adopted for characterising a wide range of other material systems possessing non-centrosymmetric point groups.
We analyse the signal formation process for scanning electron microscopic imaging applications on crystalline specimens. In accordance with previous investigations, we find nontrivial effects of incident beam diffraction on the backscattered electron distribution in energy and momentum. Specifically, incident beam diffraction causes angular changes of the backscattered electron distribution which we identify as the dominant mechanism underlying pseudocolour orientation imaging using multiple, angle-resolving detectors. Consequently, diffraction effects of the incident beam and their impact on the subsequent coherent and incoherent electron transport need to be taken into account for an in-depth theoretical modelling of the energy- and momentum distribution of electrons backscattered from crystalline sample regions. Our findings have implications for the level of theoretical detail that can be necessary for the interpretation of complex imaging modalities such as electron channelling contrast imaging (ECCI) of defects in crystals. If the solid angle of detection is limited to specific regions of the backscattered electron momentum distribution, the image contrast that is observed in ECCI and similar applications can be strongly affected by incident beam diffraction and topographic effects from the sample surface. As an application, we demonstrate characteristic changes in the resulting images if different properties of the backscattered electron distribution are used for the analysis of a GaN thin film sample containing dislocations.
We use pattern matching of experimental and dynamically simulated backscattered Kikuchi diffraction (BKD) patterns to increase the orientation precision of electron backscatter diffraction (EBSD) measurements. In order to quantify the improvement in orientation precision, we analyze the experimental distribution of the kernel average misorientation (KAM) angles. We find that for the same raw data, i.e. the same EBSD data acquisition time budget, the pattern matching approach improves the KAM resolution by an order of magnitude compared to orientation data delivered from the conventional Hough-transform based data analysis. This quantitative improvement enables us to interpret small orientation changes in plastically deformed materials which are hidden in noisy orientation data delivered from the reference EBSD system.
As an application example, we analyze a ferritic-martensitic steel (P92) sample before and after low-cycle fatigue (LCF) loading (±0.3% strain) at 620 °C. Whereas the low precision of the EBSD orientation data from the manufacturer software does not allow a reliable discrimination of the gradually changing microstructure, we find very clear systematic differences of the local microstructure after the pattern matching orientation refinement of the initial, raw pattern data. For the investigated P92 sample, the KAM-angle histograms are well described by two log-normal distributions indicating the already tempered and the remaining and mostly untempered martensite.